"i gave her a promotion given the fact she's a good employee" - correct
"I gave her a promotion once that she's a good employee" - incorrect
You could say "I gave her the promotion once that I saw she was a good employee" - but it doesn't sound as natural as the first example you gave with "given the fact".
"Once that" means when something happens or becomes known.
'I knew my firm would promote me, once that it became clear how hard I worked"
Student or Learner